Question

An electromagnetic wave, going through vacuum is
described by E = E0 sin(kx -⍵t) . Which of the following
is independent of wavelength ?
(a) k (b) ⍵
(c) k/⍵ (d) k⍵

Answer 1

Answer:

C) k / ⍵

Explanation:

The given quantities can be expressed as,

K is given by,

K = 2π / lambda

Then,

w = 2πv

c = v × lambda

w = 2π × C / lambda

K/w is guven by,

K / w = (2π/lambda) / (2πC / lambda) = 1/C

Also,

Kw = 2π/lambda × 2πC /lambda

So, k/w is an independent quantity of wavelength.

Answer 2

E = E0 sin(kx -⍵t) .

we know that,

k=2π/w

w = wavelength

⍵ =2π f

f represents frequency

we know that ,

f= c/w

⍵ =2π c /w

(a) k = 2π/w

hence ,k depends upon wavelength

(b)⍵ =2π f = 2π c/w

hence , ⍵ depends upon wavelength

(c) k/⍵ = 2π×w/2π×w ×c

k/⍵ =1 /c

k/⍵ doesn't depend upon wavelength✓

(d) k⍵ = 4π²c/w²

k⍵ depends upon wavelength